Question: Determine the value of the following complex number power. Your answer will be plotted in orange. $ ({ e^{\pi i / 2}}) ^ {7} $
Solution: Since $(a ^ b) ^ c = a ^ {b \cdot c}$ $ ({ e^{\pi i / 2}}) ^ {7} = e ^ {7 \cdot (\pi i / 2)} $ The angle of the result is $7 \cdot \frac{1}{2}\pi$ , which is $\frac{7}{2}\pi$ Our result is $ e^{3\pi i / 2}$.